Question

evaluate and write each of the following in terms of x and y.
if x= log 3 base 2
y= log 5 base 2.

i.) log 7.5 base 2
ii.) log 6750 base 2

Answer 1

Mark this answer as brainliest answer

Answer 2

Answer:

$i)log_{2}7.5=x+y-1$

$ii)log_{2}6750=1+3x+3y$

Step-by-step explanation:

$Given \: x=log_{2}3 \:---(1)$

$and\: y =log_{2}5\:---(2)$

$Now, \\i)log_{2}7.5\\</p><p>=log_{2}\frac{75}{10}\\=log_{2}\frac{15}{2}\\=log_{2}15-log_{2}2$

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By Logarithmic laws:

$i)log_{a}\frac{m}{n}=log_{a}m-log_{a}n\\ii) log_{a}a=1\\iii) log_{a}mn= log_{a}m+log_{a}n$

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$=log_{2}(3\times 5)-1\\=log_{2}3+log_{2}5-1\\=x+y-1$

$ii) log_{2}6750\\=log_{2}(2\times 3^{3}\times 5^{3}$

$=log_{2}2+log_{2}3^{3}+log_{2}5^{3}$

$=1+3log_{2}3+3log_{2}5$

$=1+3x+3y$

Therefore,

$i)log_{2}7.5=x+y-1$

$ii)log_{2}6750=1+3x+3y$

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